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In recent times, three-dimensional (3D) metamaterials have undergone arevolution driven mainly by the popularization of 3D-printing techniques, whichhas enabled the implementation of modern microwave and photonic devices withadvanced functionalities. However, the analysis of 3D metamaterials is complexand computationally costly in comparison to their 1D and 2D counterparts due tothe intricate geometries involved. In this paper, we present a fully-analyticalframework based on Floquet-Bloch modal expansions of the electromagnetic fieldsand integral-equation methods for the analysis of 3D metamaterials andmetagratings. Concretely, we focus on 3D configurations formed by periodicarrangements of rectangular waveguides with longitudinal slot insertions. Theanalytical framework is computationally efficient compared to full-wavesolutions and also works under oblique incidence conditions. Furthermore, itcomes associated with an equivalent circuit that allows to gain physicalinsight into the scattering and diffraction phenomena. The analyticalequivalent circuit is tested against full-wave simulations in commercialsoftware CST. Simulation results show that the proposed 3D structures provideindependent polarization control of the two orthogonal polarizations states.This key property is of potential interest for the production of full-metalpolarizers, such as the one illustrated.

Analytical Equivalent Circuits for Three-dimensional Metamaterials and Metagratings